Most are not. Most are 100 micrometers. Would it be sufficient?
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cevingMay 16 '13 at 14:15

The tolerance is given in the question. A child must be able to connect the bricks and they must not fall off. Which resolution is needed to achieve this?
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cevingMay 16 '13 at 14:25

Goven that all teh dimensions in en.wikipedia.org/wiki/File:Lego_dimensions.svg are in 100 micrometer increments, in theory I'd say 'yes'. In practice, I'd want to try it out on a borrowed printer before sinking large sums of money into it.
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gevMay 16 '13 at 18:14

I don't understand the question. TLG have done tons of research on this, and they are a business so they don't want to be wasting money. So if they settled for the tolerance of 10 micrometers, then a tolerance of 100 micrometers is obviously not enough. Simple as that.
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RegDwightMay 17 '13 at 11:19

1

@RegDwight Not as simple as that, since we're talking about commercial production vs DIY. Lego (and any other manufacturer of anything) can't afford to check each piece by hand, so their tolerances need to be much smaller than those of someone printing a couple of bricks at home. Even at 100 bricks a day, that would still allow you to check each brick and recycle any bad ones.
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SQBFeb 23 '14 at 20:22

The moulds are permitted a tolerance of up to two micrometres, to ensure the bricks remain connected.

But, as I noted in a comment, that is in an industrial environment, where great care is taken to ensure that not just a one-off piece is right, but that the entire batch of pieces is right. They probably take a six sigma approach or something similar.
In a DIY setting, that is not necessary. A certain percentage of faulty pieces can be tolerated, as a home manufacturer probably has the time to check each piece and recycle the faulty ones.

The image above shows the main dimensions of Lego pieces. Based on its source and the measurements given in this answer, we get 8.0mm per 20 LDU, or 0.4mm/LDU.

Since the smallest offset seen so far is 0.3 LDU, you would need at least a 0.12mm resolution to print that brick. But if you're printing pieces with a resolution of 1 LDU, you'd need a printer with at least a 1 LDU resolution.